A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

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Answer 1 · 2018-06-01T12:55:40

Longest diagonal #color(green)(d_1 = 21.88# units

Longest diagonal #d_1 = a^2 + b^2 + 2 a b cos theta#

#A_p = a b sin theta#

#A_p = 24, a = 14, b = 8#

#sin theta = 24 / (14 * 8) = 0.2143#

#theta = sin^-1 0.2143 = 0.216#

#cos theta = 0.9768#

Longest diagonal #d_1 = sqrt(14^2 + 8^2 + (2 * 14 * 8 * 0.9768))#

#color(green)(d_1 = 21.88# units

Shortest diagonal #d_2 = sqrt(14^2 + 8^2 - (2 * 14 * 8 * 0.9768))#

#color(crimson)(d_2 = 6.42# units